solve for each variable.
1. $\frac{a}{8} = -4$
2. $b - (-5) = 13$
3. $3 + \frac{18}{z} = 12$
4. $-9 + \frac{36}{a} = -5$
5. $u + 2 = -8$
6. $2z = 2$
7. $-1 - \frac{y}{8} = -7$
8. $\frac{8}{u} - (-2) = 6$
9. $a - 2 = -10$
10. $\frac{u}{6} = 3$
11. $10 - \frac{b}{2} = 3$
12. $\frac{y}{-7} = -7$
13. $\frac{b}{7} = -5$
14. $\frac{-2}{c} = 2$
15. $\frac{c}{5} + 3 = 8$

Question

Accepted Answer

### Problem 1: $\boldsymbol{\frac{a}{8} = -4}$
# Explanation:
## Step1: Multiply both sides by 8
To solve for $ a $, we multiply both sides of the equation $\frac{a}{8} = -4$ by 8. This gives us $ a = -4 \times 8 $.
## Step2: Calculate the product
Calculating $ -4 \times 8 $, we get $ a = -32 $.
# Answer:
$ a = -32 $

### Problem 2: $\boldsymbol{b - (-5) = 13}$
# Explanation:
## Step1: Simplify the left side
Simplify $ b - (-5) $ to $ b + 5 $, so the equation becomes $ b + 5 = 13 $.
## Step2: Subtract 5 from both sides
Subtract 5 from both sides: $ b = 13 - 5 $.
## Step3: Calculate the result
$ 13 - 5 = 8 $, so $ b = 8 $.
# Answer:
$ b = 8 $

### Problem 3: $\boldsymbol{3 + \frac{18}{z} = 12}$
# Explanation:
## Step1: Subtract 3 from both sides
Subtract 3 from both sides: $ \frac{18}{z} = 12 - 3 $.
## Step2: Simplify the right side
$ 12 - 3 = 9 $, so $ \frac{18}{z} = 9 $.
## Step3: Multiply both sides by $ z $
Multiply both sides by $ z $: $ 18 = 9z $.
## Step4: Divide both sides by 9
Divide both sides by 9: $ z = \frac{18}{9} $.
## Step5: Calculate the result
$ \frac{18}{9} = 2 $, so $ z = 2 $.
# Answer:
$ z = 2 $

### Problem 4: $\boldsymbol{-9 + \frac{36}{a} = -5}$
# Explanation:
## Step1: Add 9 to both sides
Add 9 to both sides: $ \frac{36}{a} = -5 + 9 $.
## Step2: Simplify the right side
$ -5 + 9 = 4 $, so $ \frac{36}{a} = 4 $.
## Step3: Multiply both sides by $ a $
Multiply both sides by $ a $: $ 36 = 4a $.
## Step4: Divide both sides by 4
Divide both sides by 4: $ a = \frac{36}{4} $.
## Step5: Calculate the result
$ \frac{36}{4} = 9 $, so $ a = 9 $.
# Answer:
$ a = 9 $

### Problem 5: $\boldsymbol{u + 2 = -8}$
# Explanation:
## Step1: Subtract 2 from both sides
Subtract 2 from both sides: $ u = -8 - 2 $.
## Step2: Calculate the result
$ -8 - 2 = -10 $, so $ u = -10 $.
# Answer:
$ u = -10 $

### Problem 6: $\boldsymbol{2z = 2}$
# Explanation:
## Step1: Divide both sides by 2
Divide both sides by 2: $ z = \frac{2}{2} $.
## Step2: Calculate the result
$ \frac{2}{2} = 1 $, so $ z = 1 $.
# Answer:
$ z = 1 $

### Problem 7: $\boldsymbol{-1 - \frac{y}{8} = -7}$
# Explanation:
## Step1: Add 1 to both sides
Add 1 to both sides: $ -\frac{y}{8} = -7 + 1 $.
## Step2: Simplify the right side
$ -7 + 1 = -6 $, so $ -\frac{y}{8} = -6 $.
## Step3: Multiply both sides by -8
Multiply both sides by -8: $ y = (-6) \times (-8) $.
## Step4: Calculate the result
$ (-6) \times (-8) = 48 $, so $ y = 48 $.
# Answer:
$ y = 48 $

### Problem 8: $\boldsymbol{\frac{8}{u} - (-2) = 6}$
# Explanation:
## Step1: Simplify the left side
Simplify $ \frac{8}{u} - (-2) $ to $ \frac{8}{u} + 2 $, so the equation becomes $ \frac{8}{u} + 2 = 6 $.
## Step2: Subtract 2 from both sides
Subtract 2 from both sides: $ \frac{8}{u} = 6 - 2 $.
## Step3: Simplify the right side
$ 6 - 2 = 4 $, so $ \frac{8}{u} = 4 $.
## Step4: Multiply both sides by $ u $
Multiply both sides by $ u $: $ 8 = 4u $.
## Step5: Divide both sides by 4
Divide both sides by 4: $ u = \frac{8}{4} $.
## Step6: Calculate the result
$ \frac{8}{4} = 2 $, so $ u = 2 $.
# Answer:
$ u = 2 $

### Problem 9: $\boldsymbol{a - 2 = -10}$
# Explanation:
## Step1: Add 2 to both sides
Add 2 to both sides: $ a = -10 + 2 $.
## Step2: Calculate the result
$ -10 + 2 = -8 $, so $ a = -8 $.
# Answer:
$ a = -8 $

### Problem 10: $\boldsymbol{\frac{u}{6} = 3}$
# Explanation:
## Step1: Multiply both sides by 6
Multiply both sides by 6: $ u = 3 \times 6 $.
## Step2: Calculate the result
$ 3 \times 6 = 18 $, so $ u = 18 $.
# Answer:
$ u = 18 $

### Problem 11: $\boldsymbol{10 - \frac{b}{2} = 3}$
# Explanation:
## Step1: Subtract 10 from both sides
Subtract 10 from both sides: $ -\frac{b}{2} = 3 - 10 $.
## Step2: Simplify the right side
$ 3 - 10 = -7 $, so $ -\frac{b}{2} = -7 $.
## Step3: Multiply both sides by -2
Multiply both sides by -2: $ b = (-7) \times (-2) $.
## Step4: Calculate the result
$ (-7) \times (-2) = 14 $, so $ b = 14 $.
# Answer:
$ b = 14 $

### Problem 12: $\boldsymbol{\frac{y}{-7} = -7}$
# Explanation:
## Step1: Multiply both sides by -7
Multiply both sides by -7: $ y = -7 \times (-7) $.
## Step2: Calculate the result
$ -7 \times (-7) = 49 $, so $ y = 49 $.
# Answer:
$ y = 49 $

### Problem 13: $\boldsymbol{\frac{b}{7} = -5}$
# Explanation:
## Step1: Multiply both sides by 7
Multiply both sides by 7: $ b = -5 \times 7 $.
## Step2: Calculate the result
$ -5 \times 7 = -35 $, so $ b = -35 $.
# Answer:
$ b = -35 $

### Problem 14: $\boldsymbol{\frac{-2}{c} = 2}$
# Explanation:
## Step1: Multiply both sides by $ c $
Multiply both sides by $ c $: $ -2 = 2c $.
## Step2: Divide both sides by 2
Divide both sides by 2: $ c = \frac{-2}{2} $.
## Step3: Calculate the result
$ \frac{-2}{2} = -1 $, so $ c = -1 $.
# Answer:
$ c = -1 $

### Problem 15: $\boldsymbol{\frac{c}{5} + 3 = 8}$
# Explanation:
## Step1: Subtract 3 from both sides
Subtract 3 from both sides: $ \frac{c}{5} = 8 - 3 $.
## Step2: Simplify the right side
$ 8 - 3 = 5 $, so $ \frac{c}{5} = 5 $.
## Step3: Multiply both sides by 5
Multiply both sides by 5: $ c = 5 \times 5 $.
## Step4: Calculate the result
$ 5 \times 5 = 25 $, so $ c = 25 $.
# Answer:
$ c = 25 $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1: $\boldsymbol{\frac{a}{8} = -4}$

Step1: Multiply both sides by 8

Step2: Calculate the product

Step1: Simplify the left side

Step2: Subtract 5 from both sides

Step3: Calculate the result

Step1: Subtract 3 from both sides

Step2: Simplify the right side

Step3: Multiply both sides by \( z \)

Step4: Divide both sides by 9

Step5: Calculate the result

Answer:

Problem 2: $\boldsymbol{b - (-5) = 13}$